Classification theorem for strong triangle blocking arrangements

2018/09/23 by Luka Milićević, Milićević, Luka
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1809.08639

22 pages, 16 figures

arxiv created 2018/09/23 · arxiv updated 2018/09/25

Abstract

A strong triangle blocking arrangement is a geometric arrangement of some line segments in a triangle with certain intersection properties. It turns out that they are closely related to blocking sets. Our aim in this paper is to prove a classification theorem for strong triangle blocking arrangements. As an application, we obtain a new proof of the result of Ackerman, Buchin, Knauer, Pinchasi and Rote which says that n points in general position cannot be blocked by n-1 points, unless n = 2,4. We also conjecture an extremal variant of the blocking points problem.

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